Specificity and randomness: structure-function relationships in neural circuits

A fundamental but unsolved problem in neuroscience is how connections between neurons might underlie information processing in central circuits. Building wiring diagrams of neural networks may accelerate our understanding of how they compute. But even if we had wiring diagrams, it is critical to know what neurons in a circuit are doing: their physiology. In both the retina and cerebral cortex, a great deal is known about topographic specificity, such as lamination and cell-type specificity of connections. Little, however, is known about connections as they relate to function. Here, we review how advances in functional imaging and electron microscopy have recently allowed the examination of relationships between sensory physiology and synaptic connections in cortical and retinal circuits.     

Estimation of the randomness of the overlapping of cellular structures

Methods for estimation of randomness of mutual overlaps of cells, their parts, and intracellular structures are developed. Two methods are proposed: a "method of areas" based on the estimation of the area of overlaps of randomly located figures, and a "method of contours" based on the evaluation of the number of intersections of linear structures located randomly. Examples are given as applied to cells and cellular nuclei, in particular during contact inhibition of cellular movement.     

K-way neural network graph partitioning with separator vertices

A neural network for partitioning graphs into any number of subgraphs using a k-way procedure is presented. The resulting neural network optimises all subgraphs so that they contain approximately the same number of vertices with the exception of a `separator' subgraph. The latter separates all the other subgraphs and is optimised to contain a minimum number of vertices. Expressions for the neuron link weights for such a network are derived analytically, and the recall mechanism of the mean field theorem neural network is used to obtain the graph partitioning. Applications focus on partitioning graphs associated with finite element meshes which, together with parallel domain decomposition solution methods, provide the motivation for this work. Received: 14 January 1998 / Accepted in revised form: 24 November 1998     

Identification of side-chain clusters in protein structures by a graph spectral method.

This paper presents a novel method to detect side-chain clusters in protein three-dimensional structures using a graph spectral approach. Protein side-chain interactions are represented by a labeled graph in which the nodes of the graph represent the Cbeta atoms and the edges represent the distance between the Cbeta atoms. The distance information and the non-bonded connectivity of the residues are represented in the form of a matrix called the Laplacian matrix. The constructed matrix is diagonalized and clustering information is obtained from the vector components associated with the second lowest eigenvalue and cluster centers are obtained from the vector components associated with the top eigenvalues. The method uses global information for clustering and a single numeric computation is required to detect clusters of interest. The approach has been adopted here to detect a variety of side-chain clusters and identify the residue which makes the largest number of interactions among the residues forming the cluster (cluster centers). Detecting such clusters and cluster centers are important from a protein structure and folding point of view. The crucial residues which are important in the folding pathway as determined by PhiF values (which is a measure of the effect of a mutation on the stability of the transition state of folding) as obtained from protein engineering methods, can be identified from the vector components corresponding to the top eigenvalues. Expanded clusters are detected near the active and binding site of the protein, supporting the nucleation condensation hypothesis for folding. The method is also shown to detect domains in protein structures and conserved side-chain clusters in topologically similar proteins.     

Quantifying the randomness of extinctions

Extinctions occur either randomly or in a more deterministic and predictable manner, with certain characteristics making some species more vulnerable to (local) extinction than others. Although the quantification of extinction randomness would better our understanding of the extinction causes and increase the predictability of future species losses, few quantification methods are currently available. To this purpose, we propose two indices based on a comparison of an a priori (expected) extinction series with an observed one. Whereas the first index requires data on the order of extinctions, the second index is only concerned with which species went extinct and which did not. Using a model for generating extinction data, we tested both indices successfully for accordance with the robustness prerequisites. Index outputs were furthermore unaffected by species richness, apart from decreased variation with rising species numbers. Because of its independence of non-extinct species and its focus on extinction sequences, the first randomness index seems especially useful for use in paleontological and paleo-ecological research. The second index is likely a good tool to study shorter term extinctions, for which the extinction order is often not known and for which the comparison with species that did persist is of greater interest. We use a real dataset to illustrate this. Finally, we discuss how it is possible to expand the use of this index toward identifying previously unknown extinction-promoting species characteristics, and toward a credible assessment of the extinction risk posed by global change.     

The necessity of connection structures in neural models of variable binding

In his review of neural binding problems, Feldman (Cogn Neurodyn 7:1–11, 2013) addressed two types of models as solutions of (novel) variable binding. The one type uses labels such as phase synchrony of activation. The other (‘connectivity based’) type uses dedicated connections structures to achieve novel variable binding. Feldman argued that label (synchrony) based models are the only possible candidates to handle novel variable binding, whereas connectivity based models lack the flexibility required for that. We argue and illustrate that Feldman’s analysis is incorrect. Contrary to his conclusion, connectivity based models are the only viable candidates for models of novel variable binding because they are the only type of models that can produce behavior. We will show that the label (synchrony) based models analyzed by Feldman are in fact examples of connectivity based models. Feldman’s analysis that novel variable binding can be achieved without existing connection structures seems to result from analyzing the binding problem in a wrong frame of reference, in particular in an outside instead of the required inside frame of reference. Connectivity based models can be models of novel variable binding when they possess a connection structure that resembles a small-world network, as found in the brain. We will illustrate binding with this type of model with episode binding and the binding of words, including novel words, in sentence structures.     

Aspects of the embryology and neural development of the American lobster.

It is feasible to study the anatomical, physiological, and biochemical properties of identifiable neurons in lobster embryos. To exploit fully the advantages of this preparation and to lay the foundation for single-cell studies, our recent goals have been to 1) establish a quantitative staging system for embryos, 2) document in detail the lobster's embryonic development, 3) determine when uniquely identifiable neurons first acquire their transmitter phenotypes, and 4) identify particular neurons that may serve developmental functions. Behavioral, anatomical, morphometric, and immunocytochemical studies have led to a detailed characterization of the growth and maturation of lobster embryos and to the adoption of a percent-staging system based upon the eye index of Perkins (Fish. Bull., 70:95-99, 1972). It is clear from these studies that the lobster nauplius molts at approximately 12% embryonic development (E12%) into a metanauplius, which subsequently undergoes a complete molt cycle within the egg. This molt cycle climaxes with the emergence of the first-stage larva shortly after hatching. Serotonin and proctolin, neurohormones widely distributed in the lobster nervous system, appear at different times in development. Serotonin immunoreactive neurons begin to appear at approximately E10%, with the adult complement being established by E50%. In contrast, proctolin immunoreactive neurons appear later and attain their full complement over a protracted period including larval and juvenile stages. The development of serotonergic deutocerebral neurons and their targets, the olfactory and accessory lobes in the brain, are also examined. The olfactory lobes are forming by E10% and have acquired their glomerular organization by E50%, whereas the formation of the accessory lobes is delayed; the early rudiments of the accessory lobes are seen by E50%, and glomeruli do not form until the second larval stage.     

The neural structures expressing perceptual hysteresis in visual letter recognition

Perception can change nonlinearly with stimulus contrast, and perceptual threshold may depend on the direction of contrast change. Such hysteresis effects in neurometric functions provide a signature of perceptual awareness. We recorded brain activity with functional neuroimaging in observers exposed to gradual contrast changes of initially hidden visual stimuli. Lateral occipital, frontal, and parietal regions all displayed both transient activations and hysteresis that correlated with change and maintenance of a percept, respectively. Medial temporal activity did not follow perception but increased during hysteresis and showed transient deactivations during perceptual transitions. These findings identify a set of brain regions sensitive to visual awareness and suggest that medial temporal structures may provide backward signals that account for neural and, thereby, perceptual hysteresis.     

Predicting secondary structures of membrane proteins with neural networks

Back-propagation, feed-forward neural networks are used to predict the secondary structures of membrane proteins whose structures are known to atomic resolution. These networks are trained on globular proteins and can predict globular protein structures having no homology to those of the training set with correlation coefficients (C) of 0.45, 0.32 and 0.43 for a-helix, -strand and random coil structures, respectively. When tested on membrane proteins, neural networks trained on globular proteins do, on average, correctly predict (Q_i) 62%, 38% and 69% of the residues in the -helix, -strand and random coil structures. These scores rank higher than those obtained with the currently used statistical methods and are comparable to those obtained with the joint approaches tested so far on membrane proteins. The lower success score for -strand as compared to the other structures suggests that the sample of -strand patterns contained in the training set is less representative than those of a-helix and random coil. Our analysis, which includes the effects of the network parameters and of the structural composition of the training set on the prediction, shows that regular patterns of secondary structures can be successfully extrapolated from globular to membrane proteins.Correspondence to: R. Casadio     

Variability and randomness in stationary neuronal activity

The patterns of neuronal activity can be different even if the mean firing rate is fixed. Investigating the variability of the firing may not be sufficient and we suggest to take into account the notion of randomness. The randomness is related to the entropy of the firing, which is bounded from above by the entropy of the Poisson process (given the mean interspike interval). Thus, we propose the Kullback-Leibler distance with respect to the Poisson process as a measure of randomness in a stationary neuronal activity. Under the condition of equal mean values the KL distance does not depend on the time scale and therefore can be compared to the coefficient of variation employed to measure the variability. Furthermore, this measure can be extended to account for correlated neuronal firing. Finally, we analyze the variability and randomness for three common ISI distributions in detail: gamma, lognormal and inverse Gaussian.     

Specificity and randomness in the visual cortex

Research on the functional anatomy of visual cortical circuits has recently zoomed in from the macroscopic level to the microscopic. High-resolution functional imaging has revealed that the functional architecture of orientation maps in higher mammals is built with single-cell precision. By contrast, orientation selectivity in rodents is dispersed on visual cortex in a salt-and-pepper fashion, despite highly tuned visual responses. Recent studies of synaptic physiology indicate that there are disjoint subnetworks of interconnected cells in the rodent visual cortex. These intermingled subnetworks, described in vitro, may relate to the intermingled ensembles of cells tuned to different orientations, described in vivo. This hypothesis may soon be tested with new anatomic techniques that promise to reveal the detailed wiring diagram of cortical circuits.     

Probing the extent of randomness in protein interaction networks

Protein-protein interaction (PPI) networks are commonly explored for the identification of distinctive biological traits, such as pathways, modules, and functional motifs. In this respect, understanding the underlying network structure is vital to assess the significance of any discovered features. We recently demonstrated that PPI networks show degree-weighted behavior, whereby the probability of interaction between two proteins is generally proportional to the product of their numbers of interacting partners or degrees. It was surmised that degree-weighted behavior is a characteristic of randomness. We expand upon these findings by developing a random, degree-weighted, network model and show that eight PPI networks determined from single high-throughput (HT) experiments have global and local properties that are consistent with this model. The apparent random connectivity in HT PPI networks is counter-intuitive with respect to their observed degree distributions; however, we resolve this discrepancy by introducing a non-network-based model for the evolution of protein degrees or "binding affinities." This mechanism is based on duplication and random mutation, for which the degree distribution converges to a steady state that is identical to one obtained by averaging over the eight HT PPI networks. The results imply that the degrees and connectivities incorporated in HT PPI networks are characteristic of unbiased interactions between proteins that have varying individual binding affinities. These findings corroborate the observation that curated and high-confidence PPI networks are distinct from HT PPI networks and not consistent with a random connectivity. These results provide an avenue to discern indiscriminate organizations in biological networks and suggest caution in the analysis of curated and high-confidence networks.     

Classification of the extracellular fields produced by activated neural structures

Background  

Classifying the types of extracellular potentials recorded when neural structures are activated is an important component in understanding nerve pathophysiology. Varying definitions and approaches to understanding the factors that influence the potentials recorded during neural activity have made this issue complex.